English

A Jordan decomposition for groups of finite Morley rank

Logic 2010-09-17 v1 Group Theory

Abstract

We prove a Jordan decomposition theorem for minimal connected simple groups of finite Morley rank with non-trivial Weyl group. From this, we deduce a precise structural description of Borel subgroups of this family of simple groups. Along the way we prove a Tetrachotomy theorem that classifies minimal connected simple groups. Some of the techniques that we develop help us obtain a simpler proof of a theorem of Burdges, Cherlin and Jaligot.

Keywords

Cite

@article{arxiv.1009.3160,
  title  = {A Jordan decomposition for groups of finite Morley rank},
  author = {Tuna Altinel and Jeffrey Burdges and Oliver Frecon},
  journal= {arXiv preprint arXiv:1009.3160},
  year   = {2010}
}